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arXiv · 2006.13508

A Limitation of the PAC-Bayes Framework

Roi Livni·Shay Moran
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Abstract

PAC-Bayes is a useful framework for deriving generalization bounds which was introduced by McAllester ('98). This framework has the flexibility of deriving distribution- and algorithm-dependent bounds, which are often tighter than VC-related uniform convergence bounds. In this manuscript we present a limitation for the PAC-Bayes framework. We demonstrate an easy learning task that is not amenable to a PAC-Bayes analysis. Specifically, we consider the task of linear classification in 1D; it is well-known that this task is learnable using just $O(\log(1/\delta)/\epsilon)$ examples. On the other hand, we show that this fact can not be proved using a PAC-Bayes analysis: for any algorithm that learns 1-dimensional linear classifiers there exists a (realizable) distribution for which the PAC-Bayes bound is arbitrarily large.

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Roi Livni, Shay Moran. 2020-06-24. A Limitation of the PAC-Bayes Framework. https://arxiv.org/abs/2006.13508

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